Date of Award

Fall 2021

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Ernst Linder

Second Advisor

Linyuan Li

Third Advisor

Jennifer Jacobs

Abstract

Regional climate simulations are often found to have significant biases. As one of the most important variables for climate change impact studies, daily precipitation simulated from regional climate models (RCMs) often exhibits excessive numbers of wet days with light rainfall, underestimated heavy rainfall values, and incorrect seasonal variations (Maraun et al., 2017). This dissertation presents three different approaches to downscale the RCM-produced daily precipitation. Unlike the traditional way of examining the zero-inflation in daily precipitation using a two-stage process, one model for the rain occurrence and the other model for rain amount conditioned on the occurrence of a wet day from the first stage, this study unifies the two processes by using a Generalized Additive Model for Location, Scale, and Shape (GAMLSS) to estimate a full-distributional climatology of daily precipitation over a single location. Then, utilizing corresponding regional climate model information, two statistical downscaling approaches are developed within the GAMLSS framework: the first one is based on a direct additive bias correction scheme, the other one is rooted in the quantile matching framework. Thereafter, a rank-based nonparametric bootstrapping technique is adopted to quantify the uncertainty in the projection of future precipitation patterns based on the developed daily rainfall models while preserving the temporal dependence of future RCM output. Results show that both approaches have a similar effect on the downscaling and the precipitation projection processes. The projected daily precipitation from these two downscaling approaches present the same wet-dry pattern, and equivalent rain amount on a wet day. As a comparison to the forementioned two downscaling approaches, a novel copula-based bias correction approach is developed to downscale the zero-inflated daily precipitation. In this approach, the joint distribution between the positive pairs of observed and RCM-produced precipitation is modeled via copulas first, next the conditional distribution of station observations conditioned on a coarse-scale RCM value is derived from the obtained joint distribution, then the conditional distribution is modified to make it discrete at zero to account for zero values. At last, stochastic rainfall simulations are performed for the future based on the modified conditional distributions. Results show the performance of this method varies in different locations. By comparing the empirical CDFs of the generated precipitations from this copula-based technique and the two GAMLSS-based approaches, the copula-based approach produces more wet days and higher rain intensity overall.

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